Bernal S D_2010.pdf - University of Plymouth

3.9 Example of belief propagation in a tree-structured network 105
3.10 Neural implementation of belief propagation in a l-'omey factor graph using the
liquid and readout neuronal populations of a liquid state machine 116
3.11 Neuronal local inference circuit (IJNC) implementing the operations of a node
in a Forney factor graph with 6 input nodes (Y,) and 6 hidden variables (X,) ... 11^
3.12 Toy example of belief propagation in Hierarchical Temporal Networks fHTM) . 124
3.13 Bayesian belief propagation architecture apphed to the visual system 127
3.14 Schematic comparison between several proposed mappings between belief propagation
and the cortical layers 136
4.1 Probabilisticinierpretationof HMAX as a Bayeslan network 146
4.2 Internal structure of a node implementing belief propagation in a Bayesian network
with a tree structure 148
4.3 Internal structure of a node implementing belief propagation in a Bayesian network
with a polytrcc structure 149
4.4 Bayesian network reproducing the structure and functionality of the 3-level
HMAX mode! 152
4.5 Bayesian network reproducing the structure and functionality of a modified version
of the 3-level HMAX model 154
4.6 Bayesian network reproducing the structure and functionality of the 4-level
HMAX model 156
4.7 Toy example illustrating how to approximate the max operation using the CPTs
between ,Sl and C'l nodes 160
4.8 Weight matrices lielween a CI node and lis afferent SI nodes 162
4.9 Toy example illustrating how to approximate the seleclivily operation using the
CPTs between CI and S2 nodes 165
4.10 Weight matrices between an S2 node and its afferent CI nodes 167
4.11 Weight matrices between a C2 node and its afferent S2 nodes 169
4.12 Weight matrix between C2 and S3 nodes forthe 3-level architecture 170
4.13 Kullback-Leibler divergence between the true and the approximate likelihood
distribution for different values i)rjW;^, 175
4.14 Problems associated with the exponential dependency on the number of parent
nodes 178
4.15 Approximation of the CI'T between a node and its multiple parents using the
weighted sum of W simpler CPTs 179
4.16 Samplingoftheparent;: messages to reduce the number of operations required
for belief propagation 180
xii